Power Method for Eigenvalues and Eigenvectors

Use the power method to iteratively find the eigenvalues and eigenvectors of a real, symmetric $5\times5$ matrix of your choice. If you don't have an orthogonalization routine, you can use the Gram-Schmidt program in the file ~s244/samples/gs.c . Also extract the eigenvalues and eigenvectors using some standard routine (NAG, EISPACK, LAPACK, etc.) and compare the results to those from using the power method, both numerically and with regard to execution time.